A deflection magnetometer is placed with its arm along the east-west direction ( tan A position) and a short bar magnet is placed symmetrically along its axis at some distance with its north pole pointing towards east. In this position the

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A deflection magnetometer is placed with its arm along the east-west direction ( tan A position) and a short bar magnet is placed symmetrically along its axis at some distance with its north pole pointing towards east. In this position the needle of the magnetometer shows a deflection of 60 ° . If we double the distance of the bar magnet, then the deflection will be

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Correct answer: C. tan - 1 ⁡ 3 8

For a short bar magnet in tan A position, μ 0 4 π 2 M d 3 = H tanθ ...(i) When distance is doubled, then new deflection θ ′ is given by, μ 0 4 π 2 M 2 d 3 = H tanθ ' ....(ii) ∴ tan ⁡ θ ′ tan ⁡ θ = 1 8 ⇒ t a n θ ′ = t a n θ 8 = tan ⁡ 60 ° 8 = 3 8 ⇒ θ ′ = tan - 1 ⁡ 3 8

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